Vectors: dot & cross product worksheet with answers

Free printable Vectors: dot & cross product worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
xy130°195°F1​F2​

Two forces act at a point in the xy-plane: F₁ = 220 N at 130° and F₂ = 270 N at 195°, both measured anticlockwise from the positive x-axis. Find the magnitude R of their resultant.

F1 = 220 N, θ1 = 130°F2 = 270 N, θ2 = 195°
R = N
2.Easy
xyza

Find the y-component ûy of the unit vector û that points in the direction of a = (−5, 3, −7).

a = (−5, 3, −7)
ûy =
3.Medium
xyzab

Find the value of k for which the vectors a = (3, −2, −2) and b = (6, −2, k) are perpendicular.

a = (3, −2, −2)b = (6, −2, k)
k =
4.Medium
xyzdFAB

A constant force F = (15, −5, 20) N acts on an object while it moves in a straight line from point A(2, 4, −5) to point B(1, 3, 1). Coordinates are in metres. Find the work W done by the force.

F = (15, −5, 20) NA(2, 4, −5) mB(1, 3, 1) m
W = J
5.Hard
xyzrFOA

A force F = (−30, −20, 30) N acts at point A(1, −1, −3). Coordinates are in metres. Find the magnitude |M| of the moment of the force about the origin O(0, 0, 0).

F = (−30, −20, 30) NA(1, −1, −3) mO(0, 0, 0) m
|M| = N·m
6.Hard
xyzABC

Find the area A of the triangle with corners A(0, 2, 2), B(3, −3, 4) and C(3, −2, 2). Coordinates are in metres.

A(0, 2, 2)B(3, −3, 4)C(3, −2, 2)
A = m²

Answer key

  1. 1. R = 414.1 N
  2. 2. ûy = 0.3293
  3. 3. k = 11
  4. 4. W = 110 J
  5. 5. |M| = 119.2 N·m
  6. 6. A = 5.22 m²

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